Chern-Simons action in noncommutative space

Abstract

We derive the noncommutative Chern-Simons action induced by Dirac fermions coupled to a background gauge field, for the fundamental, antifundamental, and the adjoint representation. We discuss properties of the noncommutative Chern-Simons action showing in particular that the Seiberg-Witten formula maps it into the standard commutative Chern-Simons action.

11 pages, 1 figure. Minor corrections, final version to be published in Physics Letters B

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• Issues of duality on non-commutative manifolds: the {\it non-equivalence} between self-dual and topologically massive models
• Maps for currents and anomalies in noncommutative gauge theories
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• Noncommutative Maxwell-Chern-Simons theory in three dimensions and its dual
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• Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings
• Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models
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• Lowest Landau level theory of the bosonic Jain states
• Noncommutative $Ad{S}^3$ with Quantized Cosmological Constant
• Maxwell-Chern-Simons Theory is Free for Marginally Noncommutative Spacetimes
• Gauge fields on noncommutative geometries with curvature
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
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• Charged rotating BTZ black holes in noncommutative spaces and torsion gravity
• Non-commutative Duality: High Spin Fields and $C{P}^1$ Model with Hopf Term
• Noncommutative Fluids
• Edge excitations of the Chern Simons matrix theory for the FQHE
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• A note on the topological order of noncommutative Hall fluids
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• Soldering Formalism in Noncommutative Field Theory: A Brief Note
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
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• On the question of regular solitons in a Noncommutative Maxwell--Chern--Simons--Higgs model
• On the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
• A note on the non-commutative Chern-Simons model on manifolds with boundary
• On The Complete Seiberg-Witten Map For Theories With Topological Terms
• Deformed "Commutative" Chern - Simons System
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• BTZ Black Hole Entropy from a Chern-Simons Matrix Model
• About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
• Seiberg-Witten map for the 4D noncommutative BF theory
• Noncommutative Wess-Zumino-Witten actions and their Seiberg-Witten invariance
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